%I #14 May 04 2021 08:48:19
%S 1,1,2,3,6,21,381,762,290703,84397476747,7122934049104967061783,
%T 14245868098209934123566,
%U 101472378935797762635619628499635817245339961,10296643686890133479148472187437767614663729545766251948487237380959682684821520304732841
%N a(0)=1, a(n+1) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) + a(6)*a(7)*a(8)*a(9) + ... + ...*a(n).
%e a(1) = a(0) = 1
%e a(2) = a(0) + a(1) = 2
%e a(3) = a(0) + a(1)*a(2) = 3
%e a(4) = a(0) + a(1)*a(2) + a(3) = 1 + 2 + 3 = 6
%e a(5) = a(0) + a(1)*a(2) + a(3)*a(4) = 1 + 2 + 18 = 21
%e a(6) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) = 1 + 2 + 18*21 = 381
%o (Python)
%o a = [1]*99
%o for n in range(20):
%o sum = i = 0
%o k = 1
%o while i<=n:
%o product = 1
%o for x in range(k):
%o product *= a[i]
%o i += 1
%o if i>n: break
%o sum += product
%o k += 1
%o a[n+1] = sum
%o print(str(a[n]),end=',')
%Y Cf. A227363, A227364, A227365, A227366.
%K nonn
%O 0,3
%A _Alex Ratushnyak_, Jul 08 2013